Citation

Abstract

This paper introduces a new multiscale framework for estimating the
tail probability of a queue fed by an arbitrary traffic process.
Using traffic statistics at a small number of time scales, our
analysis extends the theoretical concept of the critical time scale
and provides practical approximations for the tail queue probability.
These approximations are non-asymptotic; that is they apply to any
finite queue threshold. While our approach applies to any traffic
process, it is particularly apt for long-range-dependent (LRD)
traffic. For LRD fractional Brownian motion, we
prove that a sparse exponential spacing of time scales yields optimal
performance. Simulations with LRD traffic models and real Internet
traces demonstrate the accuracy of the approach. Finally, simulations
reveal that the marginals of traffic at multiple time scales have a
strong influence on queuing that is not captured well by its global
second-order correlation in non-Gaussian scenarios.